How to transform a plane into a honeycomb?
The best result (in my experience anyway) is achieved with the Tissue addon's tesselate function. The mesh isn't perfect and you need to remove doubles, but it's still much nicer and easier to use than a shrinkwrap based workflow.



What you need is a basic mesh tile that will repeat nicely, like this one:



And hopefully a fairly evenly spaced and uniform mesh, comprised of pretty much equally sized quad faces (you can generate such a mesh with the Remesh modifier).

I would suggest separating the piece you want to convert into a hex grid from the rest of the mesh, tesselate, remove doubles, then re-join with the original.

To generate the tesselation:


Select your hex tile.
Then select your target object (the one you want to generate a hex grid from).
Go to the Tissue tab in the tools panel.
Click on the "Tesselate" button.